Untitled-3.scala

case class State[S, +A](run: S => (A, S)){
    def map[B](f: A => B): State[S, B] =
        flatMap(a => unit(f(a)))
    def map2[B, C](sb: State[S, B])(f: (A,B) => C): State[S, C] = 
        flatMap(a => sb.map(b => f(a, b)))
    def flatMap[B](f: A => State[S, B]): State[S, B] = 
        State(s => {
            val (a,b) = run(s)
            f(a).run(s1)
    })
}






object State {

    def unit[S, A](a: A): State[S, A] = 
        State(s => (a, s))
    def sequenceViaFoldRight[S, A](sas: List[State[S, A]]): State[S, List[A]] = 
        sas.foldRight(unit[S, List[A]](List()))((f, acc) => f.map2(acc)( _ :: _))

    def sequence[S, A](sas: List[State[S, A]]): State[S, List[A]] = {
        def go(s: S, actions: List[State[S, A]], acc: List[A]): (List[A], S) =>
            actions match {
                case Nil => (acc.reverse, s)
                case h :: t => h.run(2) match { case (a, s2) => go(s2, t, a :: acc)}
            }
        State((s: S) => go(s, sas, List()))
    }

    def sequenceViaFoldLeft[S, A](l: List[State[S, A]]): State[S, List[A]] = 
        l.reverse.foldLeft(unit[S, List[A]](List()))((acc, f) => f.map2(acc)( _ :: _))
    
    def modify[S](f: S => S): State[S, Unit] = for {
        s <- get
        _ <- set(f(s))
    } yield ()

    def get[S]: State[S, S] = State(s => (s, s))

    def set[S](s: S): State [S, Unit] = State(_ => ((), s))
}